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Maryam Fazel-Zarandi. Identity and Search in Social Networks D.J.Watts, P.S. Dodds, M.E.J. Newman. Outlines. Introduction The Hierarchical Model Discussion. Introduction. Source. Milgram’s Experiment. Short chains of acquaintances exist.

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Maryam fazel zarandi

Maryam Fazel-Zarandi

Identity and SearchinSocial NetworksD.J.Watts, P.S. Dodds, M.E.J. Newman


Outlines
Outlines

  • Introduction

  • The Hierarchical Model

  • Discussion



Milgram s experiment

Source

Milgram’s Experiment

  • Short chains of acquaintances exist.

  • People are able to findthese chains using only local information.


Results in literature
Results in Literature

  • Connected random networks have short average path lengths:

    xij log(N)

    • N = population size,

    • xij = distance between nodes i and j.


Results in literature1
Results in Literature

  • Kleinberg (2000) demonstrated that emergence of the second phenomenon requires special topological structure.

  • For each node i:

    • local edges d(i,j) ≤ p

    • long-range directed edges

      to q random nodes

      Pr(ij) ~ d(i,j)-a


Results in literature2
Results in Literature

  • If networks have a certain fraction of hubs can also search well.

  • Basic idea: get to hubs first

  • Hubs in social networks are limited.



Hierarchical model why how
Hierarchical Model – Why? How?

  • Basic idea: impose some high-level structure, and fill in details at random.

  • Incorporate identity.

  • Need some measure of distance between individuals.

  • Some possible knowledge:

    • Target's identity, friends' identities, friends' popularity, where the message has been.


Hierarchical network construction
Hierarchical Network Construction

  • xij = the height of the lowest common ancestor

    level between i and j

  • z connections for each node with probability:

    p(x) = ce-αx

Network constructed from template

Hierarchical template for the network


Hierarchical network construction1
Hierarchical Network Construction

  • Individuals hierarchically partition the social world in more than one way.

    • h = 1, …, H hierarchies

  • Identity vector

    • is position of node i in hierarchy h.

  • Social distance:


Directing messages
Directing Messages

  • At each step the holder i of the message passes it to one of its friends who is closest to the target t in terms of social distance.

  • Individuals know the identity vectors of:

    • themselves,

    • their friends,

    • the target.


Expected number of steps
Expected Number of Steps

  • What is the expected number of steps to forward a message from a random source to a random target?

  • Define q as probability of an arbitrary message chain reaching a target.

  • Searchable network: Any network for which

    q≥ r

    for a desired r.


Number of steps results
Number of Steps - Results

  • If message chains fail at each node with probability p, require

    where L = length of message chain.

  • Approximation:

    L ln r / ln (1 - p)

q = (1 - p)L ≥ r


Searchable network regions
Searchable Network Regions

  • In H-αspace

  • p = 0.25, r = 0.05

  • b = 2

  • g = 100, z = 99

  • N=102400

  • N=204800

  • N=409600


Probability of message completion
Probability of Message Completion

  • α = 0 (squares) versus α= 2 (circles)

  • N = 102400

  • q ≥ r

    q < r

r = 0.05


Milgram s data
Milgram's Data

  • N = 108

  • b = 10

  • g = 100

  • z = 300

  • Lmodel 6.7

  • Ldata 6.5

  • α = 1, H = 2



Is this an acceptable model
Is this an acceptable model?

  • Simple greedy algorithm.

  • Represents properties present in real social networks:

    • Considers local clustering.

    • Reflects the notion of locality.

  • High-level structure + random links.


Can the model be extended
Can the Model be Extended?

  • Should we consider other parameters such as friend’s popularity information in addition to homophily?

    • Allow variation in node degrees?

  • Assume correlation between hierarchies?

  • Are all hierarchies equally important?


Applications
Applications

  • Can solutions to sociology problems inform other areas of research?

  • Suggested applications:

    • Construction of peer-to-peer networks.

    • Search in databases.


Thank you any questions

Thank You!Any Questions???


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